Domain: luther.edu
Stories and comments across the archive that link to luther.edu.
Comments · 10
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Re:Easier way to learn it
I think Geometric Algebra (GA) has a better formulation than the traditional tensor way of doing relativity. It's not only easier to understand, but it's easier to use and the same math can also be far more easily applied in other areas of physics.
A capsule: There are 4 basic dimensions, (usually denoted "e_n" with n from 0 to 3) but let's call them: x,y,z and t. The squares of the first 3 are negative, but the square of t is positive. These basis vectors can be combined to create bivectors: the regular planes of rotation xy, xz, yz, as well as xt, yt, zt. The latter three are still planes of rotation, but due to the mixed sign of the squares, the rotation is hyperbolic rather than circular - calculations use sinh and cosh instead of sin and cos. The interesting thing is that these planes of rotation involving t are velocities (Lorentz boosts). Velocities are hyperbolic rotations, and the speed of light is a 90 degree rotation. GA has a simple way of handing multiple rotations which allows easy solution of problems that are seldom even attempted using the conventional approach.
"A Survey of Geometric Algebra and Geometric Calculus" by Alan Macdonald
Gives a good introduction to the basics and applications of GA, including relativity. You would need to at least get through the section on rotations before skipping down to the section on Spacetime Algebra. Also see "General Relativity in a Nutshell"from the same author, which gives a mathematical but not dense introduction to General Relativity in 100 pages, not using GA."Gravity, Gauge Theories and Geometric Algebra" by Anthony Lasenby, Chris Doran, Stephen Gull
General Relativity using GA - interestingly, curved space-time is not required using GA."Primer on Geometric Algebra for introductory mathematics and physics" by David Hestenes
Another good intro, much less dense than Macdonald's, with more diagrams and basic applications."Geometric Algebra Primer" by Jaap Suter
Gives a gentle introduction and reference for the basic GA operations."3D Euclidean Geometry through Conformal Geometric Algebra (a GAViewer tutorial)" by Leo Dorst & Daniel Fontijne
Gives a hands-on, step-by-step tutorial using the free open-source GA visualization software GA Viewer. This tutorial uses the conformal model which is more advanced than the regular 3-D model. Other tutorials are available at the same site. Their book Geometric Algebra for Computer Science, an Object Oriented Approach to Geometry" is also highly recommended, and can be previewed at Scribd. -
Re:Easier way to learn it
I think Geometric Algebra (GA) has a better formulation than the traditional tensor way of doing relativity. It's not only easier to understand, but it's easier to use and the same math can also be far more easily applied in other areas of physics.
A capsule: There are 4 basic dimensions, (usually denoted "e_n" with n from 0 to 3) but let's call them: x,y,z and t. The squares of the first 3 are negative, but the square of t is positive. These basis vectors can be combined to create bivectors: the regular planes of rotation xy, xz, yz, as well as xt, yt, zt. The latter three are still planes of rotation, but due to the mixed sign of the squares, the rotation is hyperbolic rather than circular - calculations use sinh and cosh instead of sin and cos. The interesting thing is that these planes of rotation involving t are velocities (Lorentz boosts). Velocities are hyperbolic rotations, and the speed of light is a 90 degree rotation. GA has a simple way of handing multiple rotations which allows easy solution of problems that are seldom even attempted using the conventional approach.
"A Survey of Geometric Algebra and Geometric Calculus" by Alan Macdonald
Gives a good introduction to the basics and applications of GA, including relativity. You would need to at least get through the section on rotations before skipping down to the section on Spacetime Algebra. Also see "General Relativity in a Nutshell"from the same author, which gives a mathematical but not dense introduction to General Relativity in 100 pages, not using GA."Gravity, Gauge Theories and Geometric Algebra" by Anthony Lasenby, Chris Doran, Stephen Gull
General Relativity using GA - interestingly, curved space-time is not required using GA."Primer on Geometric Algebra for introductory mathematics and physics" by David Hestenes
Another good intro, much less dense than Macdonald's, with more diagrams and basic applications."Geometric Algebra Primer" by Jaap Suter
Gives a gentle introduction and reference for the basic GA operations."3D Euclidean Geometry through Conformal Geometric Algebra (a GAViewer tutorial)" by Leo Dorst & Daniel Fontijne
Gives a hands-on, step-by-step tutorial using the free open-source GA visualization software GA Viewer. This tutorial uses the conformal model which is more advanced than the regular 3-D model. Other tutorials are available at the same site. Their book Geometric Algebra for Computer Science, an Object Oriented Approach to Geometry" is also highly recommended, and can be previewed at Scribd. -
Re:Easier way to learn it
I think Geometric Algebra (GA) has a better formulation than the traditional tensor way of doing General Relativity. It's not only easier to understand, but it's easier to use and the same math can also be far more easily applied in other areas of physics.
A capsule: There are 4 basic dimensions, (usually denoted "e_n" with n from 0 to 3) but let's call them: x,y,z and t. The squares of the first 3 are negative, but the square of t is positive. These basis vectors can be combined to create bivectors: the regular planes of rotation xy, xz, yz, as well as xt, yt, zt. The latter three are still planes of rotation, but due to the mixed sign of the squares, the rotation is hyperbolic rather than circular - calculations use sinh and cosh instead of sin and cos. The interesting thing is that these planes of rotation involving t are velocities (Lorentz boosts). Velocities are hyperbolic rotations, and the speed of light is a 90 degree rotation. GA has a simple way of handing multiple rotations which allows easy solution of problems that are seldom even attempted using the conventional approach.
"A Survey of Geometric Algebra and Geometric Calculus" by Alan Macdonald
Gives a good introduction to the basics and applications of GA, including relativity. You would need to at least get through the section on rotations before skipping down to the section on Spacetime Algebra. Also see "General Relativity in a Nutshell"from the same author, which gives a mathematical but not dense introduction to General Relativity in 100 pages, not using GA."Gravity, Gauge Theories and Geometric Algebra" by Anthony Lasenby, Chris Doran, Stephen Gull
General Relativity using GA - interestingly, curved space-time is not required using GA."Primer on Geometric Algebra for introductory mathematics and physics" by David Hestenes
Another good intro, much less dense than Macdonald's, with more diagrams and basic applications."Geometric Algebra Primer" by Jaap Suter
Gives a more gentle introduction and reference for the basic GA operations."3D Euclidean Geometry through Conformal Geometric Algebra (a GAViewer tutorial)" by Leo Dorst & Daniel Fontijne
Gives a hands-on, step-by-step tutorial using their free open-source GA visualization software, "GAViewer". This tutorial uses the conformal model which is more advanced than the regular 3-D model. (2 extra dimensions, of a very odd but useful type) Other tutorials are available at the same site. Their book Geometric Algebra for Computer Science, an Object Oriented Approach to Geometry" is also highly recommended, and can be previewed at Scribd. (The 2nd edition is worth getting on paper. It has some very useful reference pages not available online, and many corrected errata.) -
Re:Easier way to learn it
I think Geometric Algebra (GA) has a better formulation than the traditional tensor way of doing General Relativity. It's not only easier to understand, but it's easier to use and the same math can also be far more easily applied in other areas of physics.
A capsule: There are 4 basic dimensions, (usually denoted "e_n" with n from 0 to 3) but let's call them: x,y,z and t. The squares of the first 3 are negative, but the square of t is positive. These basis vectors can be combined to create bivectors: the regular planes of rotation xy, xz, yz, as well as xt, yt, zt. The latter three are still planes of rotation, but due to the mixed sign of the squares, the rotation is hyperbolic rather than circular - calculations use sinh and cosh instead of sin and cos. The interesting thing is that these planes of rotation involving t are velocities (Lorentz boosts). Velocities are hyperbolic rotations, and the speed of light is a 90 degree rotation. GA has a simple way of handing multiple rotations which allows easy solution of problems that are seldom even attempted using the conventional approach.
"A Survey of Geometric Algebra and Geometric Calculus" by Alan Macdonald
Gives a good introduction to the basics and applications of GA, including relativity. You would need to at least get through the section on rotations before skipping down to the section on Spacetime Algebra. Also see "General Relativity in a Nutshell"from the same author, which gives a mathematical but not dense introduction to General Relativity in 100 pages, not using GA."Gravity, Gauge Theories and Geometric Algebra" by Anthony Lasenby, Chris Doran, Stephen Gull
General Relativity using GA - interestingly, curved space-time is not required using GA."Primer on Geometric Algebra for introductory mathematics and physics" by David Hestenes
Another good intro, much less dense than Macdonald's, with more diagrams and basic applications."Geometric Algebra Primer" by Jaap Suter
Gives a more gentle introduction and reference for the basic GA operations."3D Euclidean Geometry through Conformal Geometric Algebra (a GAViewer tutorial)" by Leo Dorst & Daniel Fontijne
Gives a hands-on, step-by-step tutorial using their free open-source GA visualization software, "GAViewer". This tutorial uses the conformal model which is more advanced than the regular 3-D model. (2 extra dimensions, of a very odd but useful type) Other tutorials are available at the same site. Their book Geometric Algebra for Computer Science, an Object Oriented Approach to Geometry" is also highly recommended, and can be previewed at Scribd. (The 2nd edition is worth getting on paper. It has some very useful reference pages not available online, and many corrected errata.) -
Re:You asked a guide?
I guess my school was somewhat unusual: I was a tour guide, a senior (I don't even think they hire freshman), and just happened to be a CS major. Alas, nobody asked me about Linux--but if they did, I would have been able to tell them we had a Linux lab (although only for CS majors/minors or people in CS courses), a local mirror of several OSS projects (most notably Ubuntu), and that--while we used mostly Windows with a few Macs--our IT department was quite friendly to Linux and open-source in general. (Our online course management system was based on Moodle; we actually hired people to contribute to the project so we could make better use of it.)
The only problem I had with Linux was trying to find a working driver for my wireless network adapter--and that definitely wasn't my school's fault. (In general, I'd say if the school supports at least Macs besides just Windows, Linux shouldn't be ridiculously difficult to get at least most computing-related goodies to work...awkard required software [you could use a VM for that if Wine doesn't work] and network-registration requirements [hopefully they aren't dumb enough to think people use only Windows and OS X and require verification software that runs only on these two OSes] aside.)
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Re:It all makes sense
Maybe my area isn't the norm, but we have a lot more private colleges here (midwest, specifically Iowa) than public ones (or were you thinking only of high schools--do some of them really use these systems?). My school made the switch to Moodle this year after years of using Blackboard--although they *did* come up with their own name for it because they probably couldn't keep a straight face telling their students to go to Moodle (their name is Kaite, spelled with various degrees of capitalization and periods or with a lack thereof, for "Knowledge and Technology in Education" and a play on the fact that this is Luther College and Luther's wife was named Katie).
Granted, I was never here when they used Blackboard, but I don't think I've heard many complaints about Moodle.
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Re:bittorrent
The school I am looking at for next year (Luther College) blocks all P2P traffic, as I found out this summer. They're not a tech school, and it's unfortunate because I was hoping I could maybe download a Linux distro or two that users torrents (Xandros). However, I guess there are still plenty that don't, so I shouldn't be too left out. And I would do it from home, but BB isn't available here.
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Don't Fret
I am a programmer, and I suck at math. I've always been able to get through it but I'm horrible at it, it doesn't "click" with me, and I've had to work hard and long to get through any problems whatsoever.
I took Calculus I through a community college affiliation while a senior in HS. I did all right...B+/A- average. Nothing spectacular, and I had to really bust my butt to get it.
Upon arriving at college I enrolled in CalcII and was blown away within 4 weeks because of the vast chasm between the two classes, let alone how quickly the concepts of CalcI left my mind. I quickly dropped it and was much disheartened.
My advisor said I would need to start over; I had to have higher maths in order to be a computer programmer. I was frustrated and very depressed...computers came extremely easy, maths did not. I felt Very Screwed(tm).
Then I was visiting another CS professor in his office, a brilliant man, and we got talking about it. He said it was bullshit; if you've had algebra and geometry and a basic understanding of trig, unless you were going into game programming, advanced research, or something like AI, you didn't need more than that. Enlightened, I gave up trying to do higher maths and never did another class in them in college.
And you know what? I've never, never needed what I don't have. The concepts and ideas I've retained from algebra, geometry, trig, and basic math have covered my ass more times than I dare say, and concepts in computer science have crossed any gaps that existed (discrete structures, etc.) I have no doubt that if I pursue a higher degree in CS that I'll need to take some or if I decided to get into graphics or such.
Remember: Your education isn't as much as WHAT you know but that you know how to LEARN what you need to know. Develop your skill to be able to figure things out on your own and you'll prosper more than trying to remember vague abstract theories and theorms. -
Caveats and SuggestionsLots of good posts here already, so I'll try not to duplicate. This is a list of my caveats and suggestions, having done 4 years already.
- Pen, not pencil. Pencil is for people who aren't confident. J/k. You'll be grateful for the scribbles, trust me. More than once a mis-written scribble saved my ass. Write lots of stuff in the margins, even if it's completely offtopic. You'll laugh about them later when you read them.
- Capabilities. Make sure you know what your campus network will allow. The college that I attended has its residential network completely separated from the labs -- you can't connect from one to the other. I had to send emails to myself if I wanted to move information. A pain in the ass...be prepared for such things being implemented.
- Fun and Games. One of the best uses computers had in college was fun. And I'm not talking about Quake. This is different fun -- webcams, mp3 jukeboxes, IM'ing your roommate from a different room to go get you a beer, computing on the shitter. Things like that. Make sure your system is flexible. Linux helps.
- Portable Storage - I never really had this other than zipdisks. A thumbdrive would have been great...moving files around, since networks weren't hooked together, was a real bitch. Much easier to take some sort of media around.
- Cheap Laptop w/Wireless. - I would recommend in addition to a nice desktop to buy a cheap, used, low-power laptop. Battery complete, wireless if you can afford it, 100' long cable if you can't. You know NOT the true pleasures in life until you can drag your laptop out onto the lawn on a bright sunny spring day, write a term paper, chat online, surf the web, ask your roommate back inside on the couch to bring you another beer, and watch damn cute girls play sand volleyball in bikinis at the same time. TRUST ME on this one.
- Power Button - For the monitor or the box, I don't care. College is one of (if not the) best times of your life. I miss it horribly. Be sure to shut off that box or monitor and get your ass outside, to parties, on a bench with a girl late at night, doing crazy, half-illegal shit with your friends and roommates. You won't wish you had more screen time, but you'll wish you had more of the other things.
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American Colleges, not all BadFrom the: I-could've-swore-you-said-you-knew-assembly dept.
I went to a four-year college and do not feel that a) my time was wasted, or b) I came out with an overinflated ego. I realize now that college did not teach me how to do computers, it taught me how to be a human being in a lot of ways, and also gave me the bare tools to be able to teach myself any technology that I would care to pick up.
The problem that most people out of college have is that:- The system insists that to get a job, you must have a 3.0, or 3.5 or higher GPA. Period. I did not graduate with a 3.0 or higher. And because of this, there were IT companies that wouldn't even look at my resume, let alone give me a chance to prove that I knew something or was trainable. I came to like companies that did not use numbers to define me.
However, the push to have good grades is still very high, so colleges inflate the "average" level up to a B, B+, or A- and suddenly everyone is doing well. Amazing. - The advertisements for job openings offer such odd and hard-to-get requirements, you must try and fabricate anything you can to get those on your resume somehow. I hadn't had formal, professional HTML design, but had done it for a few years for myself and others, so I put that down. I had a one-semester class in Smalltalk, so I put that down. I once taught the IP protocol to a hamster, so I wrote that down. Egos are often driven by the industry's demands on what you have to have. Honesty would be a big help here.
- The system insists that to get a job, you must have a 3.0, or 3.5 or higher GPA. Period. I did not graduate with a 3.0 or higher. And because of this, there were IT companies that wouldn't even look at my resume, let alone give me a chance to prove that I knew something or was trainable. I came to like companies that did not use numbers to define me.